I used to have one of those. Mine was a 1980. When I got it the governor was disconnected and it went like a bat out of hell. I put the governor back on after the daughters rolled it.
I'd agree that your problem is carb/fuel system. If you have the same carburetor I had it has an integral vacuum operated fuel pump - the thing is similar to a chain saw or weed whip. That aftermarket electric pump raises all sorts of red flags. The carburetor needs to be set up properly, order a rebuild kit and the service manual from the link in the next paragraph.
Parts are readily available for the engine/carburetor. This guy has most everything: http://www.golfcartcare.com/. I got a piston and rings from him when I rebuilt the top end and various other parts from time to time.
I had trouble with it being hard to start after sitting - the fuel line would drain back into the tank. Turns out there is supposed to be a check valve in the tank on the fuel pick up. It was a commodity item I ordered through my local small engine shop.